Can we identify Walrasian allocations?

[eng] We consider a discrete time, pure exchange infinite horizon economy with two or more consumers and at least one concumption good per period. Within the framework of decentralized mechanisms, we show that for a given consumption trade at any period of time, say at time one, the consumers will need, in general, an infinite dimensional (informational) space to identigy such a trade as an intemporal Walrasian one. However, we show and characterize a set of enviroments where the Walrasian trades at each period of time can be achieved as the equilibrium trades of a sequence of decentralized competitive mechanisms, using only both current prices and quantities to coordinate decisions.

Aggregation of liposomes induced by calcium: A structural and kinetic study

In this work, the calcium-induced aggregation of phosphatidylserine liposomes is probed by means of the analysis of the kinetics of such process as well as the aggregate morphology. This novel characterization of liposome aggregation involves the use of static and dynamic light-scattering techniques to obtain kinetic exponents and fractal dimensions. For salt concentrations larger than 5 mM, a diffusion-limited aggregation regime is observed and the Brownian kernel properly describes the time evolution of the diffusion coefficient. For slow kinetics, a slightly modified multiple contact kernel is required. In any case, a time evolution model based on the numerical resolution of Smoluchowski's equation is proposed in order to establish a theoretical description for the aggregating system. Such a model provides an alternative procedure to determine the dimerization constant, which might supply valuable information about interaction mechanisms between phospholipid vesicles.

Análisis de convergencia de las regiones de la zona euro (1990-2010)

Since the birth of Economic and Monetary Union (EMU), policies have been implemented in the Member States of the European Union (EU) to lead them towards economic convergence. This article analyses the convergence of the 174 regions that exist in the 17 euro-zone countries in the years from 1990 to 2010. The article specifies a space-time econometric model using the hypotheses of conditioned beta-convergence and sigmaconvergence. The dependent variables of the model are per capita GDP and productivity and the explanatory variables are real economic variables. Beta-convergence is found to exist between the countries of the euro-zone in terms of per capita GDP, but there is divergence in terms of productivity, though only at country level. In other words, the hypothesis is confirmed that it is guidelines at country level that lead to hypothetical convergence and that the unfavourable performance of productivity is due, without doubt, to differences in behaviour between the active populations of the different euro zone countries

Wigner higher-order spectra: definition, properties, computation and application to transient signal analysis

The Wigner higher order moment spectra (WHOS)are defined as extensions of the Wigner-Ville distribution (WD)to higher order moment spectra domains. A general class oftime-frequency higher order moment spectra is also defined interms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to theproperties of WHOS which are, in fact, extensions of the properties of the WD. Discrete time and frequency Wigner higherorder moment spectra (DTF-WHOS) distributions are introduced for signal processing applications and are shown to beimplemented with two FFT-based algorithms. One applicationis presented where the Wigner bispectrum (WB), which is aWHOS in the third-order moment domain, is utilized for thedetection of transient signals embedded in noise. The WB iscompared with the WD in terms of simulation examples andanalysis of real sonar data. It is shown that better detectionschemes can be derived, in low signal-to-noise ratio, when theWB is applied.

Unidirectional quantum walks: Evolution and exit times

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the currently widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in place or move in a fixed direction, e.g., rightward or upward. While both formulations are essentially equivalent, the present approach leads us to consider discrete Fourier transforms, which eventually results in obtaining explicit expressions for the wave functions in terms of finite sums and allows the use of efficient algorithms based on the fast Fourier transform. The wave functions here obtained govern the probability of finding the particle at any given location but determine as well the exit-time probability of the walker from a fixed interval, which is also analyzed.

Revenue management under general discrete choice model of consumer behavior

Customer choice behavior, such as 'buy-up' and 'buy-down', is an importantphe-nomenon in a wide range of industries. Yet there are few models ormethodologies available to exploit this phenomenon within yield managementsystems. We make some progress on filling this void. Specifically, wedevelop a model of yield management in which the buyers' behavior ismodeled explicitly using a multi-nomial logit model of demand. Thecontrol problem is to decide which subset of fare classes to offer ateach point in time. The set of open fare classes then affects the purchaseprobabilities for each class. We formulate a dynamic program todetermine the optimal control policy and show that it reduces to a dynamicnested allocation policy. Thus, the optimal choice-based policy caneasily be implemented in reservation systems that use nested allocationcontrols. We also develop an estimation procedure for our model based onthe expectation-maximization (EM) method that jointly estimates arrivalrates and choice model parameters when no-purchase outcomes areunobservable. Numerical results show that this combined optimization-estimation approach may significantly improve revenue performancerelative to traditional leg-based models that do not account for choicebehavior.

Forecasting volatility using a continuous time model

This paper evaluates the forecasting performance of a continuous stochastic volatility model with two factors of volatility (SV2F) and compares it to those of GARCH and ARFIMA models. The empirical results show that the volatility forecasting ability of the SV2F model is better than that of the GARCH and ARFIMA models, especially when volatility seems to change pattern. We use ex-post volatility as a proxy of the realized volatility obtained from intraday data and the forecasts from the SV2F are calculated using the reprojection technique proposed by Gallant and Tauchen (1998).

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Applications of stochastic analysis in finance and statistical inference

First: A continuous-time version of Kyle's model (Kyle 1985), known as the Back's model (Back 1992), of asset pricing with asymmetric information, is studied. A larger class of price processes and of noise traders' processes are studied. The price process, as in Kyle's model, is allowed to depend on the path of the market order. The process of the noise traders' is an inhomogeneous Lévy process. Solutions are found by the Hamilton-Jacobi-Bellman equations. With the insider being risk-neutral, the price pressure is constant, and there is no equilibirium in the presence of jumps. If the insider is risk-averse, there is no equilibirium in the presence of either jumps or drifts. Also, it is analised when the release time is unknown. A general relation is established between the problem of finding an equilibrium and of enlargement of filtrations. Random announcement time is random is also considered. In such a case the market is not fully efficient and there exists equilibrium if the sensitivity of prices with respect to the global demand is time decreasing according with the distribution of the random time. Second: Power variations. it is considered, the asymptotic behavior of the power variation of processes of the form _integral_0^t u(s-)dS(s), where S_ is an alpha-stable process with index of stability 0&alpha&2 and the integral is an Itô integral. Stable convergence of corresponding fluctuations is established. These results provide statistical tools to infer the process u from discrete observations. Third: A bond market is studied where short rates r(t) evolve as an integral of g(t-s)sigma(s) with respect to W(ds), where g and sigma are deterministic and W is the stochastic Wiener measure. Processes of this type are particular cases of ambit processes. These processes are in general not of the semimartingale kind.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Discrete devaluations and multiple equilibria in a first generation model of currency crises

The first generation models of currency crises have often been criticized because they predict that, in the absence of very large triggering shocks, currency attacks should be predictable and lead to small devaluations. This paper shows that these features of first generation models are not robust to the inclusion of private information. In particular, this paper analyzes a generalization of the Krugman-Flood-Garber (KFG) model, which relaxes the assumption that all consumers are perfectly informed about the level of fundamentals. In this environment, the KFG equilibrium of zero devaluation is only one of many possible equilibria. In all the other equilibria, the lack of perfect information delays the attack on the currency past the point at which the shadow exchange rate equals the peg, giving rise to unpredictable and discrete devaluations.

Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Among the underlying assumptions of the Black-Scholes option pricingmodel, those of a fixed volatility of the underlying asset and of aconstantshort-term riskless interest rate, cause the largest empirical biases. Onlyrecently has attention been paid to the simultaneous effects of thestochasticnature of both variables on the pricing of options. This paper has tried toestimate the effects of a stochastic volatility and a stochastic interestrate inthe Spanish option market. A discrete approach was used. Symmetricand asymmetricGARCH models were tried. The presence of in-the-mean and seasonalityeffectswas allowed. The stochastic processes of the MIBOR90, a Spanishshort-terminterest rate, from March 19, 1990 to May 31, 1994 and of the volatilityofthe returns of the most important Spanish stock index (IBEX-35) fromOctober1, 1987 to January 20, 1994, were estimated. These estimators wereused onpricing Call options on the stock index, from November 30, 1993 to May30, 1994.Hull-White and Amin-Ng pricing formulas were used. These prices werecomparedwith actual prices and with those derived from the Black-Scholesformula,trying to detect the biases reported previously in the literature. Whereasthe conditional variance of the MIBOR90 interest rate seemed to be freeofARCH effects, an asymmetric GARCH with in-the-mean and seasonalityeffectsand some evidence of persistence in variance (IEGARCH(1,2)-M-S) wasfoundto be the model that best represent the behavior of the stochasticvolatilityof the IBEX-35 stock returns. All the biases reported previously in theliterature were found. All the formulas overpriced the options inNear-the-Moneycase and underpriced the options otherwise. Furthermore, in most optiontrading, Black-Scholes overpriced the options and, because of thetime-to-maturityeffect, implied volatility computed from the Black-Scholes formula,underestimatedthe actual volatility.

On the relevance of modeling volatility for pricing purposes

This paper presents a two-factor (Vasicek-CIR) model of the term structure of interest rates and develops its pricing and empirical properties. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread. Assuming a certain process for both factors, a general bond pricing equation is derived and a closed-form expression for bond prices is obtained. Empirical evidence of the model's performance in comparisson with a double Vasicek model is presented. The main conclusion is that the modeling of the volatility in the long-term rate process can help (in a large amount) to fit the observed data can improve - in a reasonable quantity - the prediction of the future movements in the medium- and long-term interest rates. However, for shorter maturities, it is shown that the pricing errors are, basically, negligible and it is not so clear which is the best model to be used.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).